arXiv subjects
Publications and source records attributed to Samuel Desrochers.
In this paper, we study the list object functor $L : \mathcal{C} \rightarrow \mathcal{C}$ for a general category $\mathcal{C}$ with finite limits and parametrized list objects. We show that $L$ is polynomial as long as $\mathcal{C}$ is extensive.
Following some work done by Komjath and Schmerl, we extend the definition of a cloud to $\mathbb{R}^N$ for $N \geq 2$ and show that $k$ clouds cover $\mathbb{R}^2$ if and only if $k$ clouds cover $\mathbb{R}^N$. We also show that countably many clouds cover $\mathbb{R}^N$.